On the existence of generalised syzygies in the planar three-body problem
We consider the Newtonian planar three-body problem. One defines a generalised syzygy as a configuration where the three bodies or their velocities become collinear. Assuming that the motion is bounded and collision-free, we provide a simple sufficient condition for the existence of such configurati...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2023-01-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.409/ |
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| author | Tsygvintsev, Alexei |
| author_facet | Tsygvintsev, Alexei |
| author_sort | Tsygvintsev, Alexei |
| collection | DOAJ |
| description | We consider the Newtonian planar three-body problem. One defines a generalised syzygy as a configuration where the three bodies or their velocities become collinear. Assuming that the motion is bounded and collision-free, we provide a simple sufficient condition for the existence of such configurations. Our proof is elementary and uses only basic tools from the Sturm–Liouville theory. |
| format | Article |
| id | doaj-art-45e63b2fadf542a4834969d00268adeb |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-45e63b2fadf542a4834969d00268adeb2025-02-07T11:06:07ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-01-01361G133133510.5802/crmath.40910.5802/crmath.409On the existence of generalised syzygies in the planar three-body problemTsygvintsev, Alexei0https://orcid.org/0000-0002-8744-4100ENS de Lyon, UMPA, 46 allée d’Italie, 69364 Lyon Cedex 07, FRANCEWe consider the Newtonian planar three-body problem. One defines a generalised syzygy as a configuration where the three bodies or their velocities become collinear. Assuming that the motion is bounded and collision-free, we provide a simple sufficient condition for the existence of such configurations. Our proof is elementary and uses only basic tools from the Sturm–Liouville theory.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.409/ |
| spellingShingle | Tsygvintsev, Alexei On the existence of generalised syzygies in the planar three-body problem Comptes Rendus. Mathématique |
| title | On the existence of generalised syzygies in the planar three-body problem |
| title_full | On the existence of generalised syzygies in the planar three-body problem |
| title_fullStr | On the existence of generalised syzygies in the planar three-body problem |
| title_full_unstemmed | On the existence of generalised syzygies in the planar three-body problem |
| title_short | On the existence of generalised syzygies in the planar three-body problem |
| title_sort | on the existence of generalised syzygies in the planar three body problem |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.409/ |
| work_keys_str_mv | AT tsygvintsevalexei ontheexistenceofgeneralisedsyzygiesintheplanarthreebodyproblem |